One-Dimensional Electronic States in a Moir\'e Superlattice of Twisted Bilayer WTe2

Abstract

One-dimensional (1D) moir\'e superlattices provide a new route to engineering reduced-dimensional electronic states in van der Waals materials, yet their electronic structure and microscopic origin remain largely unexplored. Here, we investigate the structural relaxation and electronic properties of a 1D moir\'e superlattice formed in twisted bilayer 1T$'$-WTe$_2$ using density functional theory calculations, complemented by high-angle annular dark-field scanning transmission electron microscopy. We show that lattice relaxation strongly reconstructs the moir\'e stripes, leading to stacking-dependent stripe widths that are in excellent agreement with experimental observations. The relaxed structure hosts quasi-one-dimensional electronic bands near the Fermi level, characterized by strong dispersion along the stripe direction and nearly flat dispersion in the perpendicular direction. By comparing the full bilayer with isolated relaxed layers, we establish that these 1D electronic states are governed predominantly by an intralayer moir\'e potential induced by in-plane lattice relaxation, rather than by interlayer hybridization. We extract this position-dependent moir\'e potential directly from DFT calculations and construct an effective tight-binding model that reproduces both the band dispersion and the real-space localization of the electronic wave functions. Our results identify lattice relaxation as the key mechanism underlying 1D electronic states in 1D moir\'e superlattices. %and establish twisted bilayer WTe$_2$ as a promising platform for exploring emergent one-dimensional moir\'e physics. The framework developed here provides a unified theoretical basis for realizing and exploring one-dimensional moir\'e physics in a broad class of anisotropic two-dimensional materials.